Parametric Study of a Two-dimensional Membrane Wing in Viscous Laminar Flow

Abstract

A computational study of a two-dimensional membrane at low Reynolds numbers is presented. The membrane is assumed to be linearly elastic, massless and practically of zero thickness. A parametric study of the eects of membrane properties, tension, and ow conditions is presented for both steady and unsteady cases. The membrane shape and aerodynamic forces are computed by a fully viscous ow model and compared to those computed with a potential model. Steady results, obtained for small angles of attack (AoA), show that the membrane AoA and tension coecient uniquely dene the membrane equilibrium shape for both potential and viscous ow (for prescribed Reynolds number). Thus, the membrane initial slack, elasticity and pretension, which are used to compute the tension coecient, do not play an independent role in the steady cases. In these cases the parametric study concentrates on the eect of the membrane tension coecient, angle of attack, Reynolds number and shear stress. Results show that the tension coecient highly aects the membrane camber, while the AoA mostly inuences the chordwise location of the maximum camber point. The shear stress eect on the equilibrium shape was found to be negligible, and an increase in Reynolds number resulted in stall conditions at smaller AoA. The unsteady solutions, computed for large AoAs, present oscillations of the membrane structure which are due to vortex shedding. In these cases the eects of membrane elasticity, slack, pretension, angle of attack and Reynolds number are studied.